Until I began to investigate, I naively assumed that Jesus thought of himself as a "Christian" more than a Jew. And I didn't view the early Christians as composed in part of Jews, who continued to be Jewish while embracing Jesus as the promised Messiah. That's why I've found the Complete Jewish Bible (CJB), a modern English version of the Old and New Testaments, to be such an interesting resource.
Reading this version feels like traveling through a foreign country with the aid of a local guide, instead of trying to understand everything simply by reading a guidebook. For instance, non-Jewish readers might be interested to learn that the "hem" of Jesus' garment, which a woman touched when reaching out for healing, See Matt. 9:20 . was actually a ritual tassel that Jewish men are instructed by the Torah to wear as a reminder to obey God's commandments.
The CJB is full of renderings aimed at restoring the original Jewish underpinnings of the New Testament. The book of Hebrews, for instance, is called "Messianic Jews," and many other book names are so revised. Translator David H. Stern also uses original Hebrew names for people such as Jesus (Yeshua), and places such as Jerusalem (Yerushalayim). Thus, you might have a local guide with the CJB, but you would still need your foreign language dictionary while reading the story mentioned above to understand that a tzitzit is a "ritual tassel." (Fortunately, there is an index in the back.)